Entropy Production Research Articles

LOSS BREAKDOWN IN AXIAL TURBINES: A NEW METHOD FOR VORTEX LOSS AND WAKE DETECTION FROM 3D RANS SIMULATIONS

Abstract To enhance turbine efficiency, it is essential to mitigate the losses generated by irreversible phenomena in turbine flows, including boundary layers, shock waves, vortices, and trailing edge wakes. Fast and accurate detection of losses is crucial from the earliest design stages, where reduced-order models based on oversimplified correlations are employed. This requires a deep understanding of the physics behind loss-generating mechanisms, attainable by examining the 3D flow. While existing criteria can identify various phenomena, accurately quantifying vortex-generated losses remains challenging, as these losses frequently extend beyond the vortical structure. This paper provides a straightforward and effective approach to localize and assess vortex-related losses. The method is grounded in Zlatinov's decomposition of the entropy generation rate into a streamwise and secondary flow component. A criterion based on vortex kinematics evaluates the vortex's strength, enabling the determination of its spatial influence and contribution to overall losses. To validate the method, a post-processing code is developed to perform loss breakdown, using existing identification criteria and new techniques introduced within this work, particularly for wake detection. 3D RANS simulations on various configurations, from simple curved ducts to nozzle guide vanes, allow to gradually test and validate the computational tool. Results confirm that the highest entropy generation rates occur outside the vortical structure and show good ability to identify both the vortex shape and its area of influence in terms of losses. A significant improvement in predicting vortex losses is observed, especially for turbine blades with leakage vortices.

Entropy generation and soret phenomenon on hydromagnetic oscillatory convective-dissipative thermally radiative flow of a chemically reactive liquid across a permeable surface

Entropy generation and soret phenomenon on hydromagnetic oscillatory convective-dissipative thermally radiative flow of a chemically reactive liquid across a permeable surface

Entropy generation outcomes in peristalsis of Carreau–Yasuda nanofluid flow with activation energy

AbstractThis paper focuses on the study of activation energy and entropy generation in the peristaltic flow of a Carreau–Yasuda nanofluid. Peristaltic transport, coupled with entropy generation and activation energy in a curved geometry, has significant applications in biomedical and industrial processes involving non‐Newtonian fluids. Blood flow in the arteries, the movement of chyme in the gastrointestinal tract, and peristaltic motion replicate the natural muscular contractions that drive fluid flow in the physiological systems. The integration of entropy generation allows for the evaluation of energy efficiency and the analysis of losses due to viscous dissipation. Activation energy plays a crucial role in processes such as drug delivery, where temperature‐sensitive reactions or biochemical changes affect fluid behavior. In industrial applications, like peristaltic pumps in chemical reactors or polymer processing, the consideration of entropy and activation energy aids in optimizing thermal management and reaction rates. The mathematical model is developed under these assumptions, and the governing equations are numerically solved using the NDSolve function in Mathematica. Graphical results show that higher activation energy and concentration reduce the reaction rate, while the Bejan number and entropy generation increase with a larger Brinkman number. Velocity and temperature increase under slip conditions, whereas concentration decreases, and a stronger radial magnetic field reduces both velocity and the size of the trapped bolus.

Entropy generation in radiative motion of tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms and activation energy

In this work, entropy generation is optimized through the application of the second law of thermodynamics. The slip mechanisms, Brownian diffusions, and thermophoresis are elaborated using the tangent hyperbolic nanomaterial model. Magnetohydrodynamic (MHD) fluid is taken into consideration. To characterize the impact of activation energy, a unique model involving the binary chemical reaction is deployed. The effects of mixed convection that is nonlinear in nature, bioconvection, and Joule effect are all taken into consideration. The key partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by utilizing appropriate similarity transformations and then solved numerically with the help of a built-in ‘bvp4c’ technique of MATLAB software. Varied flow parameters’ impacts on the nanoparticle volume concentration, entropy number, microorganism concentration, temperature, and velocity fields are analyzed using graphs. Various flow variables are taken into consideration to calculate the total rate of entropy generation. The obtained results show that concentration irreversibility, Joule effect irreversibility, viscous dissipation, and heat irreversibility all influence the entropy. The numerical outcomes were observed by fixing the physical parameters as 0.1<α<4.0, 0.1<M<1.2, 0.1<Nr<2.2, 0.1<Le<2.2, 0.1<Nb<0.4, 0.1<Nt<1.0, 2.0<⁡Pr⁡<5.0, and 0.1<Lb<2.0, as well as their impact on the momentum, thermal, concentration, and microorganism density profiles. From results, an increasing estimate of the variable representing chemical reaction indicates a decline in the concentration. The higher the chemical reaction variable, Hartmann number, and Weissenberg number, the higher the entropy number, while the Bejan number has a contrary behavior. Subsequently, all the outcomes are plotted in graphs and discussed in detail, when subjected to the involving physical quantities.

Thermal–Hydraulic Performance Analysis of Combined Heat Sink with Open Microchannels and Embedded Pin Fins

An open type of microchannel with diamond pin fins (OM-DPFs) is introduced for the cooling of high-performance electronic chips. For a Reynolds number (Re) of 247~1173, a three-dimensional model is established to explore the hydrothermal properties of the OM-DPF and compare it to traditional heat sinks with closed rectangular microchannels (RMs), heat sinks with open microchannels (OMs), and the results in the existing research. Firstly, the synergy between tip clearance and pin fins on the hydrothermal properties is discussed. Secondly, the entropy production principle is adopted to analyze the irreversible losses for different heat sinks. Lastly, the total efficiencies of different heat sinks are assessed. The RMs present the worst heat transfer with the lowest friction loss. For the OMs, the temperature and pressure drop are decreased slightly compared to those of the RMs, and the irreversible loss is reduced by 4% at Re = 1173 because of the small tip clearance. But the total efficiency is lower than that of the RMs because the pressure drop advantage is offset by the weak heat transfer. For the OM-DPF, the combined structure has a noticeable impact on the multiple physical fields and hydrothermal characteristics, which present the best thermal performance at the cost of the highest friction loss. The irreversible loss of heat transfer in the OM-DPF is reduced obviously, but the friction irreversible loss significantly increases at high Re values. At Re = 429, the total entropy production of the OM-DPF is reduced by 47.57% compared with the RM. Compared to the OM and the single-pin fin structure in the literature, the total efficiency of the OM-DPF is increased by 14.56% and 40.32% at Re = 614. For a pump power of 0.1 W, the total thermal resistance (Rth) of the OM-DPF is dropped by 23.77% and 21.19% compared to the RM and OM. For a similar Rth, the pump power of the combined structure is 63.64% and 42.86% lower than that of the RM and OM. Thus, the novel combined heat sink can achieve efficient heat removal while controlling the energy consumption of liquid cooling systems, which has bright application prospects.

Initially reactive and concentrated generalized fluid wavy flow with the applications of disorder theory and magnetic field: A computational study

The wavy flow of generalized fluid namely, Cross fluid is mathematically formulated on a gravitationally affected vertical wavy surface with significant physical effects which is the main theme of this work. This particular dynamics of chemically reactive materials is further explored with an irreversible process. A significant heat transfer is measured through thermal resistance during the consideration of entropy optimization. Since entropy generation is associated with the mechanical systemenergy loss is more helpful in monitoring the entropy production in different engineering and industrial processes. Specifically, such irreversibility process appearance causing a noticeable low efficiency in the relevant practical sectors. For better performance in the minimization of friction on the wavy surface, flow is dissipated in terms of heat. However, the measure of loss in terms of work is introduced in the form of thermal radiation, viscous dissipation, magnetic field, and first-order chemical reaction. Additionally, the expected pressure drooping on the wavy surface is another goal of the entire study. The non-linear mathematical equations are determined by following the maximum viscosity approach. Relevant and important results are portrayed to show the various features of the newly developed work. The significant findings are approximated via one of the collocation methods while using MATLAB software. The Richardson number and buoyancy parameter enhanced the flow speed of the materials. The heat transfer rate is decreased by both Eckert number and wavy amplitude and the chemical reaction factor enhanced the mass transfer rate. The heat energy of the materials is escalated with the help of electromagnetic wave radiation and temperature ratio factor. Strengthening the chemical reaction factor declined the mass flow during the typical motion of the liquid. In the last, a comparison is provided to show the accuracy of the numerical approach.

Second law and Liu relations: the no-reversible-direction axiom—revisited

AbstractA thermodynamic process is governed by balance equations in field-formulated thermodynamics. Especially the balance equation of entropy takes a prominent role: it introduces the Second Law in the form of a dissipation inequality via the non-negative entropy production. Balance equations and dissipation inequality are independent of the considered material which is described by additional constitutive equations which need the introduction of a state space which is spanned by the state space variables. Inserting these constitutive equations into the balance equations results in the balance equations on state space which include the first order time and position derivatives of the state space variables, called “higher derivatives” wich are directional derivatives in a mathematicle sense. Why do not appear the latter in the Liu Relations which pretend to describe material as well as the equations on state space do ? The answer is that the Liu Relations describe materials whose entropy production does not depend on the higher derivatives. Consequently, the Liu Relations are more specific than the balance equations on state space. A toy example concerning heat conduction in compressible fluids is in two different versions added for elucidation.

Computational outline on heat transfer analysis and entropy generation in hydromagnetic squeezing slip flow of hybrid nanofluid

PurposeThe current work investigates an unsteady squeezed flow of hybrid-nanofluid between two parallel plates in occurrence with a uniform transverse magnetic field. Water is used as base fluid mixed with Graphene Oxide (GO) and Copper (Cu) nanoparticles. The flow considered here is under slip boundary conditions.Design/methodology/approachThe governing PDEs are transmuted into ODEs by applying an appropriate similarity transformation and then solved numerically using the 4th order R-K method with shooting technique. Graphical illustrations for velocity, temperature, entropy generation (NG), Bejan number (Be), streamline etc. are presented and discussed in detail from the physical point of view. The nature of the Nusselt number is also studied numerically through contour plots for different flow parameters.FindingsThere is no funding obtained for the research work.Social implicationsThis kind of study may be used in various fields including polymer processing, lubrication apparatus, compression including hydrodynamical machines compression, food processing etc.Originality/valueIt is observed that very little investigation has yet been made about the movement of hybrid nanofluid between two analogous plates.

Computational analysis of unsteady oscillatory flow of nanofluid with variable electric conductivity: gear-generalized differential quadrature approach

Abstract This study numerically investigated the entropy production in nanofluids’ dissipative unsteady oscillatory flow characterized by variable electric conductivity and magnetic heating effects. The imposition of the non-isothermal boundary condition on the oscillatory stretching sheet plays a crucial role in establishing the self-similar solution in the presence of viscous heating. An external magnetic field (uniform in space and time) is imposed perpendicular to the plane of the oscillating stretched boundary. The energy equation, incorporating viscous dissipation effects and momentum equation, is reduced to nonlinear coupled partial differential equations and numerically solved using the Gear-generalized differential quadrature scheme.Additionally, to ensure the precision and reliability of the outcomes, the numerical code undergoes a thorough validation process that involves comparing its outputs to the findings of previous available studies. The Corcione model is implemented to describe the nanofluid’s effective viscosity and thermal conductivity. Furthermore, expressions for entropy production and relative irreversibility parameter (Bejan number), considering variable electric conductivity, are derived and computed based on solutions obtained from momentum and energy equations. The impacts of parameters such as magnetic parameter, variable electric conductivity parameter, Eckert number, Strouhal number, Prandtl number and temperature difference parameters on flow, heat transfer, entropy generation, and Bejan number are systematically illustrated and examined. We observed that increasing the variable electric conductivity parameters reduces the velocity profiles while improving the thermal fields. Similar behavior is found when the strength of a magnetic field is increased. The skin friction coefficient exhibits an augmentation in response to the Eckert number, dimensionless time, Strouhal number, nanoparticle volume fraction, magnetic parameter, and variable thermal conductivity parameter. Conversely, the Nusselt number increases concerning the Strouhal number and nanoparticle volume fraction. At the same time, it declines in association with the magnetic parameter, dimensionless time, Eckert number, and variable electric conductivity parameter.This comprehensive investigation enhances our understanding of nanofluid dynamics and provides valuable insights for optimizing thermal management systems across various engineering disciplines.

A Study on the Evolution Laws of Entrainment Performances Using Different Mixer Structures of Ejectors

Being the core of the ejector refrigeration system, an ejector with a suitable mixer, conical–cylindrical or cylindrical, is key to high-energy-efficiency and low-carbon systems. To promote the scientific selection of mixers for ejectors based on the theoretical models that have been validated by experiments, the evolution laws of the entrainment ratios in the two types of ejectors are studied under various operating conditions. Furthermore, the influence mechanism of the mixer structures on the entrainment ratio of the ejector is elucidated by comparing the distribution characteristics of the entropy generation rate, pressure lift proportion, and entropy generation rate of the per-unit pressure lift in the two types of ejectors. The efficiencies of the conical-cylindrical mixer ejector and cylindrical mixer ejector exist a crossover, which makes the entrainment ratio of the conical–cylindrical mixer ejector smaller under small compression ratios but larger under large compression ratios. By changing the cylindrical mixer into a conical one, on the one hand, more pressure rise will be distributed in the diffuser, which helps to reduce the entropy increase rate in the pressurization process; on the other hand, the wall impulse effect of the conical mixer will lead to an increase in entropy generation rate of per-unit pressure lift, resulting in a growing entropy generation rate of boosting. The dominant roles are not the same with changing compression ratios, which leads to different relationships of entrainment ratio between the cylindrical and conical mixer ejectors.

Cold-Atom Particle Collider

A major objective of the strong ongoing drive to realize quantum simulators of gauge theories is achieving the capability to probe collider-relevant physics on them. In this regard, a highly pertinent and sought-after application is the controlled collisions of elementary and composite particles, as well as the scattering processes in their wake. Here, we propose particle-collision experiments in a cold-atom quantum simulator for a 1+1D (one spatial and one temporal dimension) U(1) lattice gauge theory with a tunable topological θ term, where we demonstrate an experimentally feasible protocol to impart momenta to elementary (anti)particles and their meson composites. We numerically benchmark the collisions of moving wave packets for both elementary and composite particles, uncovering a plethora of rich phenomena, such as oscillatory string dynamics in the wake of elementary (anti)particle collisions due to confinement. We also probe string inversion and entropy production processes across Coleman’s phase transition through far-from-equilibrium quenches. We further demonstrate how collisions of composite particles unveil their internal structure. Our work paves the way towards the experimental investigation of collision dynamics in state-of-the-art quantum simulators of gauge theories, and sets the stage for microscopic understanding of collider-relevant physics in these platforms. Published by the American Physical Society 2024

Heat Transfer and Entropy Generation on Free Convection Airflow inside a T-shaped Cavity Considering Inner Obstacles

In this study, a numerical analysis of heat and entropy generation on free convection of airflow is performed inside a T-shaped cavity with and without circular obstacles. The T-shaped cavity is formed with two symmetrically isothermal rectangular blocks. A cold temperature is maintained on the cavity's upper wall. The adiabatic walls are connected to heated wall at constant temperature. It is assumed that the flow is laminar, 2-D, and steadily incompressible. The finite element analysis is employed for solving the governing equations. The calculated results are compared and validated with the other published works. The dimensionless velocity (streamlines) and temperature (isotherms) are calculated and illustrated for varying Rayleigh numbers. It is found that the average Nusselt number at the heated walls and entropy generation inside the cavity increase with the increment of Rayleigh numbers. Moreover, the thermal performance effects on natural convection flow are investigated with circular obstacles inside the enclosure. Five cases without and with circular obstacles regarding the boundary conditions are investigated. It is found that the thermal performance of the cavity can be improved by adding two circular obstacles with cool boundary conditions. It is evident that the innovative structure by adding two circular obstacles with cool boundary conditions gives higher average Nusselt number and entropy generation whereas lower Bejan numbers for varying Rayleigh numbers. The study is performed for and . Jagannath University Journal of Science, Volume 11, Number 1, June 2024, pp. 186−202

Comparative analysis of buoyancy-driven hydromagnetic flow and heat transfer in a partially heated square enclosure using Cu-Fe3O4 and MoS2-Fe3O4 nanofluids

Purpose This study aims to investigate entropy generation through natural convection and examine heat transfer properties within a partially heated and cooled enclosure influenced by an angled magnetic field. The enclosure, subjected to consistent heat production or absorption, contains a porous medium saturated with a hybrid nanofluid blend of Cu-Fe3O4 and MoS2-Fe3O4. Design/methodology/approach The temperature and velocity equations are converted to a dimensionless form using suitable non-dimensional quantities, adhering to the imposed constraints. To solve these transformed dimensionless equations, the finite-difference method, based on the MAC (Marker and Cell) technique, is used. Comprehensive numerical simulations address various control parameters, including nanoparticle volume fraction, Rayleigh number, heat source or sink, Darcy number, Hartmann number and slit position. The results are illustrated through streamlines, isotherms, average Nusselt numbers and entropy generation plots, offering a clear visualization of the impact of these parameters across different scenarios. Findings Results obtained show that the Cu-Fe3O4 hybrid nanofluid exhibits higher entropy generation than the MoS2-Fe3O4 hybrid nanofluid when comparing them at a Rayleigh number of 106 and a Darcy number of 10–1. The MoS2 hybrid nanofluid demonstrates a low permeability, as evidenced by an average Darcy number of 10–3, in comparison to the Cu hybrid nanofluid. The isothermal contours for a Rayleigh number of 104are positioned parallel to the vertical walls. Additionally, the quantity of each isotherm contour adjacent to the hot wall is being monitored. The Cu and MoS2 nanoparticles exhibit the highest average entropy generation at a Rayleigh number of 105 and a Darcy number of 10–1, respectively. When a uniform heat sink is present, the temperature gradient in the central part of the cavity decreases. In contrast, the absence of a heat source or sink leads to a more intense temperature distribution within the cavity. This differs significantly from the scenario where a uniform heat sink regulates the temperature. Originality/value The originality of this study is to examine the generation of entropy in natural convection within a partially heated and cooled enclosure that contains hybrid nanofluids. Partially heated corners are essential for optimizing heat transfer in a wide range of industrial applications. This enhancement is achieved by increasing the surface area, which improves convective heat transfer. These diverse applications encompass fields such as chemical engineering, mechanical engineering, surface research, energy production and heat recovery processes. Researchers have been working on improving the precision of heated and cold corners using various methods, such as numerical, experimental and analytical approaches. These efforts aim to enhance the broad utility of these corners further.

Numerical simulation of phase transition with the hyperbolic Godunov-Peshkov-Romenski model

In this paper, a thermodynamically consistent numerical solution of the interfacial Riemann problem for the first-order hyperbolic continuum model of Godunov, Peshkov and Romenski (GPR model) is presented. In the presence of phase transition, interfacial physics are governed by molecular interaction on a microscopic scale, beyond the scope of the macroscopic continuum model in the bulk phases. The developed approximate two-phase Riemann solvers tackle this multi-scale problem, by incorporating a local thermodynamic model to predict the interfacial entropy production. Using phenomenological relations of non-equilibrium thermodynamics, interfacial mass and heat fluxes are derived from the entropy production and provide closure at the phase boundary. We employ the proposed Riemann solvers in an efficient sharp interface level-set Ghost-Fluid framework to provide coupling conditions at phase interfaces under phase transition. As a single-phase benchmark, a Rayleigh-Bénard convection is studied to compare the hyperbolic thermal relaxation formulation of the GPR model against the hyperbolic-parabolic Euler-Fourier system. The novel interfacial Riemann solvers are validated against molecular dynamics simulations of evaporating shock tubes with the Lennard-Jones shifted and truncated potential. On a macroscopic scale, evaporating shock tubes are computed for the material n-Dodecane and compared against Euler-Fourier results. Finally, the efficiency and robustness of the scheme is demonstrated with shock-droplet interaction simulations that involve both phase transfer and surface tension, while featuring severe interface deformations.

System response time and optimal path

Abstract In this work we study, in general terms, the optimal path for an out-of-equilibrium process from a geometric perspective constructed from a probability density function belonging to the exponential family (PDFE). With this objective we have constructed the speed of entropy production for a system out of equilibrium. This speed of entropy production is not determined with respect to the clock time t but rather with respect to a dimensionless time ξ (t) associated with a characteristic response time of each system λ (t). In this context, we demonstrate that the constant entropy production speed condition leads to the system moving on a geodesic of the manifold constructed from the probability density function. In the last part of this work we apply our general results to study the Ornstein–Uhlenbeck process (OU), which is a well-known stochastic process that strictly speaking describes the velocity of a Brownian particle under the influence of friction. As the system evolves we find that dimensionless time ξ (t) passes slower than clock time t.

Irreversibility analysis of radiative TiO2+Al2O3+Cu/H2O ternary nanofluid flow over a bidirectional stretching sheet with cattaneo-christov heat flux: nanotechnology applications

Ternary nanofluids demonstrate better heat transfer characteristics in contrast to conventional liquids and typical hybrid nanofluids. These are applied in sophisticated cooling systems for electronics, heat exchangers, and automotive engines, along with renewable energy systems such as solar collectors, where efficient heat transfer plays a crucial role. The aim of this research is to investigate the movement of a Casson ternary nanofluid passing through a bidirectional exponential sheet by employing the innovative Cattaneo-Christov heat flux concept. The utilization of the energy equation considers thermal radiation, viscous dissipation, and heat source/sink effects, with the integration of chemical reaction effects into the concentration equation. An analysis of entropy generation is utilized to evaluate the thermodynamic irreversibility within the system. The conversion of transport equations involves a transformation from partial to ordinary differential equations, followed by a numerical solution utilizing the BVP4C solver embedded in the MATLAB package R2022b. The impacts of developed factors on thermal, concentration, and velocity behavior, as well as engineering quantities, are thoroughly explored graphically. The outcome reveals that the velocity gradients diminish as magnetic fields intensify, while it amplified by the Hall factor. The rise in temperature of ternary nanofluid correlates with elevated levels of radiation, and Brownian motion. Concentration intensifies with the rapid development of thermophoresis influences. Heightened values of the Reynolds and Brinkman numbers give rise to amplified entropy production but a decrease in the Bejan number. The ternary nanofluid displays a remarkable 8.92% increase in skin friction on the x-axis and y-axis, influenced by the potent Darcy-Forchheimer factor. The rates of mass and heat transfer in nanofluids undergo a decrease of 8.58% and 12.52%, respectively, due to the heightened influence of Brownian motion and Eckert number. The results could provide valuable insights into the performance of ternary nanofluids in various industrial environments under specific conditions.

The Relationship Between Astronomical and Developmental Times Emerging in Modeling the Evolution of Agents.

The simplest evolutionary model for catching prey by an agent (predator) is considered. The simulation is performed on the basis of a software-emulated Intel i8080 processor. Maximizing the number of catches is chosen as the objective function. This function is associated with energy dissipation and developmental time. It is shown that during Darwinian evolution, agents with an initially a random set of processor commands subsequently acquire a successful catching skill. It is found that in the process of evolution, a logarithmic relationship between astronomical and developmental times arises in agents. This result is important for the ideas available in the literature about the close connection of such concepts as time, Darwinian selection, and the maximization of entropy production.

Analysis of Entropy Optimization in MHD Flow of Non-Newtonian Nanofluids with Chemical Reaction and Thermal Energies

Investigation of nanofluid flows under various conditions is becoming fascinating research due to its numerous applications in many science and engineering fields such as solar energy, geothermal energy, water purification, glass blowing, enhanced oil recovery, petroleum production and food processing. For the present requirements in thermal energy applications, this mathematical model is considered to explore the diffusion and heat source effects on the flow of conductive Casson and Maxwell nanofluids in a porous medium on an elongating sheet with a chemical reaction. Further, the effects of viscous dissipation and thermal radiation are also examined. Moreover, the entropy generation is analyzed since this approach is employed in solar energy exchangers. The governing equations and the corresponding boundary conditions are constructed. This system of partial differential equations (PDEs) is changed into a system of nonlinear ordinary differential equations (ODEs) with the help of a suitable transformation and then solved numerically by the bvp5c MATLAB package. The influences of the physical parameters on the flow phenomena are discussed and presented through figures and tables. This analysis explains that the Casson fluid flow has a higher velocity field than the Maxwell fluid flow. The Nusselt number becomes higher as the Dufour numbers increase. It has also been noticed that increasing the Brinkmann number improves the entropy and, an increase in radiation enriches the temperature profile. The concentration of the fluid is decreased for the increasing values of the higher-order chemical reaction parameter. Furthermore, comparisons of the current results were conducted for limiting examples of the problem and found to be in good agreement with existing results in the literature.

Entropy generation analysis and thermal performance of absorber tube in parabolic trough solar collector inserted with eccentric structure insert

To address the issue of uneven heat transfer in parabolic trough solar collectors, this study introduces an innovative insert (composed of vortex generators) layout. The vortex generators are strategically placed in areas with high heat flux density, while their number is reduced in regions with low heat flux density. By adjusting the position of the central rod, the inserts are defined as three different layout strategies (central structure, low eccentric structure, and upper eccentric structure), and their thermal performance is analyzed. The differences in fluid flow and heat transfer induced by different structures are also compared. The results show that the upper eccentric structure can induce unevenly distributed high-intensity mixing vortices, and through the ejection and sweeping movements of these vortices, the high-temperature fluid in areas with high heat flux density is transported to positions with low geothermal flow. Among all the studied configurations, the upper eccentric structure achieves a Nusselt number increase ranging from 1.16 to 2.34 times and a friction number value increase between 1.47 and 5.38 times. In terms of heat transfer performance, the highest value is 1.43 when the number of vortex generators is 6 and Reynold number is 13,750. Additionally, the thermal performance of the inserted tubes is analyzed using the field synergy principle and entropy generation method.

Analysis of Flow Loss Characteristics of a Multistage Pump Based on Entropy Production

To reveal the internal flow loss characteristics of a multi-stage pump, the unsteady calculation of the internal flow field of a seven-stage centrifugal pump was carried out, and the entropy production theory and Q criterion were utilized to analyze the unsteady flow characteristics of each flow component under different flow rates. The research results show that as the flow rate increases, the entropy production value and the energy loss inside the flow components also increase accordingly. The viscous dissipation entropy production caused by fluid viscosity is very small, and the turbulent dissipation entropy production caused by turbulent fluctuations and wall dissipation entropy production are the main sources of energy loss. The impellers, diffusers, and outlet chamber are the main regions of energy loss in the multistage pump. The entropy production value of the first-stage impeller is significantly higher than that of other impellers, while the entropy production value of the first-stage diffuser is significantly lower than that of other diffusers. Through vortex structure analysis, it is found that the high entropy production regions in the impeller are concentrated in the impeller inlet area, the blade suction surface, and the impeller outlet area.